Higher Siegel–Weil formula for unitary groups: the non-singular terms

Abstract

We construct special cycles on the moduli stack of hermitian shtukas. We prove an identity between (1) the

r th

$r^{\mathrm{th}}$ central derivative of non-singular Fourier coefficients of a normalized Siegel–Eisenstein series, and (2) the degree of special cycles of “virtual dimension 0” on the moduli stack of hermitian shtukas with

r

$r$ legs. This may be viewed as a function-field analogue of the Kudla-Rapoport Conjecture, that has the additional feature of encompassing all higher derivatives of the Eisenstein series.